

A316111


a(n) is the smallest k > 1 such that gcd(k, n^k  n) = 1, for n > 1.


1



35, 35, 77, 77, 143, 55, 55, 77, 119, 119, 35, 55, 187, 143, 77, 35, 35, 77, 143, 247, 95, 35, 77, 77, 77, 55, 55, 143, 77, 77, 35, 35, 247, 143, 143, 35, 35, 77, 77, 143, 55, 95, 119, 119, 77, 35, 55, 143, 143, 77, 35, 35, 119, 299, 221, 55, 35, 77, 77, 77, 55, 55, 187, 119
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OFFSET

2,1


COMMENTS

Conjecture: all the terms are in A121707. If k is a term, then k is an "antiCarmichael number": p1 does not divide k1 for every prime p dividing k.
The sequence is unbounded, since a(m!) > m.
Prediction: a(n) < n for all sufficiently large n.
GCD(n, a(n)) = 1. a(n) is odd. Is a(n) squarefree?  David A. Corneth, Aug 13 2018


LINKS



PROG

(PARI) a(n) = {my(k=2); while (gcd(k, n^k  n) != 1, k++); k; } \\ Michel Marcus, Aug 13 2018
(PARI) a(n) = {my(k=3); while (gcd(k, n^k  n) != 1, k+=2; while(gcd(n, k) > 1, k+=2)); k} \\ David A. Corneth, Aug 13 2018


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



